A perspective is taken on the intangible complexity of economic and social systems by investigating the underlying dynamical processes that produce, store and transmit information in financial time series in terms of the textit{moving average cluster
entropy}. An extensive analysis has evidenced market and horizon dependence of the textit{moving average cluster entropy} in real world financial assets. The origin of the behavior is scrutinized by applying the textit{moving average cluster entropy} approach to long-range correlated stochastic processes as the Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Fractional Brownian motion (FBM). To that end, an extensive set of series is generated with a broad range of values of the Hurst exponent $H$ and of the autoregressive, differencing and moving average parameters $p,d,q$. A systematic relation between textit{moving average cluster entropy}, textit{Market Dynamic Index} and long-range correlation parameters $H$, $d$ is observed. This study shows that the characteristic behaviour exhibited by the horizon dependence of the cluster entropy is related to long-range positive correlation in financial markets. Specifically, long range positively correlated ARFIMA processes with differencing parameter $ dsimeq 0.05$, $dsimeq 0.15$ and $ dsimeq 0.25$ are consistent with textit{moving average cluster entropy} results obtained in time series of DJIA, S&P500 and NASDAQ.
We present an error band on neutron matter properties at finite temperature (finite-T) which comprehends uncertainties on the nuclear interaction, the many-body method convergence, and the thermodynamical consistency of the approach. This study provi
des nonperturbative predictions for finite-T neutron matter employing chiral interactions which are selected on the basis of their performance in both finite nuclei and infinite matter at zero temperature. Since proper theoretical uncertainties at finite-T are still generally lacking, the band provided here represents a first step towards setting first-principles constraints on thermal aspects of the nuclear matter equation of state.
We study if commonly used nucleon-nucleon effective interactions, obtained from fitting the properties of cold nuclear matter and of finite nuclei, can properly describe the hot dense nuclear matter produced in intermediate-energy heavy-ion collision
s. We use two representative effective interactions, i.e., an improved isospin- and momentum-dependent interaction with its isovector part calibrated by the results from the emph{ab initio} non-perturbative self-consistent Greens function (SCGF) approach with chiral forces, and a Skyme-type interaction fitted to the equation of state of cold nuclear matter from chiral effective many-body perturbation theory and the binding energy of finite nuclei. In the mean-field approximation, we evaluate the equation of state and the single-nucleon potential for nuclear matter at finite temperatures and compare them to those from the SCGF approach. We find that the improved isospin- and momentum-dependent interaction reproduces reasonably well the SCGF results due to its weaker momentum dependence of the mean-field potential than in the Skyrme-type interaction. Our study thus indicates that effective interactions with the correct momentum dependence of the mean-filed potential can properly describe the properties of hot dense nuclear matter and are thus suitable for use in transport models to study heavy-ion collisions at intermediate energies.
We exploit the many-body self-consistent Greens function method to analyze finite-temperature properties of infinite nuclear matter and to explore the behavior of the thermal index used to simulate thermal effects in equations of state for astrophysi
cal applications. We show how the thermal index is both density and temperature dependent, unlike often considered, and we provide an error estimate based on our ${it ab~initio}$ calculations. The inclusion of many-body forces is found to be critical for the density dependence of the thermal index. We also compare our results to a parametrization in terms of the density dependence of the nucleon effective mass. Our study questions the validity of predictions made for the gravitational-wave signal from neutron-star merger simulations with a constant thermal index.
We present first-principle predictions for the liquid-gas phase transition in symmetric nuclear matter employing both two- and three-nucleon chiral interactions. Our discussion focuses on the sources of systematic errors in microscopic quantum many b
ody predictions. On the one hand, we test uncertainties of our results arising from changes in the construction of chiral Hamiltonians. We use five different chiral forces with consistently derived three-nucleon interactions. On the other hand, we compare the ladder resummation in the self-consistent Greens functions approach to finite temperature Brueckner--Hartree--Fock calculations. We find that systematics due to Hamiltonians dominate over many-body uncertainties. Based on this wide pool of calculations, we estimate that the critical temperature is $T_c=16 pm 2$ MeV, in reasonable agreement with experimental results. We also find that there is a strong correlation between the critical temperature and the saturation energy in microscopic many-body simulations.
A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked according to the
ir size to form a probability distribution function and finally fed in the expression of the Shannon entropy. In this work, such entropy measure is implemented on the time series of prices and volatilities of six financial markets. The analysis has been performed, on tick-by-tick data sampled every minute for six years of data from 1999 to 2004, for a broad range of moving average windows and volatility horizons. The study shows that the entropy of the volatility series depends on the individual market, while the entropy of the price series is practically a market-invariant for the six markets. Finally, a cumulative information measure - the `Market Heterogeneity Index- is derived from the integral of the proposed entropy measure. The values of the Market Heterogeneity Index are discussed as possible tools for optimal portfolio construction and compared with those obtained by using the Sharpe ratio a traditional risk diversity measure.
We present the fundamental techniques and working equations of many-body Greens function theory for calculating ground state properties and the spectral strength. Greens function methods closely relate to other polynomial scaling approaches discussed
in chapters 8 and 10. However, here we aim directly at a global view of the many-fermion structure. We derive the working equations for calculating many-body propagators, using both the Algebraic Diagrammatic Construction technique and the self-consistent formalism at finite temperature. Their implementation is discussed, as well as the inclusion of three-nucleon interactions. The self-consistency feature is essential to guarantee thermodynamic consistency. The pairing and neutron matter models introduced in previous chapters are solved and compared with the other methods in this book.
The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or space. In this
paper, mainly based on analytical arguments, the scaling performances of the centered DMA, including higher-order ones, are investigated by means of a continuous time approximation and a frequency response approach. Our results are also confirmed by numerical tests. The study is carried out for higher-order DMA operating with moving average polynomials of different degree. In particular, detrending power degree, frequency response, asymptotic scaling, upper limit of the detectable scaling exponent and finite scale range behavior will be discussed.
The properties of symmetric nuclear and pure neutron matter are investigated within an extended self-consistent Greens function method that includes the effects of three-body forces. We use the ladder approximation for the study of infinite nuclear m
atter and incorporate the three-body interaction by means of a density-dependent two-body force. This force is obtained via a correlated average over the third particle, with an in-medium propagator consistent with the many-body calculation we perform. We analyze different prescriptions in the construction of the average and conclude that correlations provide small modifications at the level of the density-dependent force. Microscopic as well as bulk properties are studied, focusing on the changes introduced by the density dependent two-body force. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sum rule. Our results validate previously used uncorrelated averages and extend the availability of chirally motivated forces to a larger density regime.
The present thesis aims at studying the properties of symmetric nuclear and pure neutron matter from a Greens functions point of view, including two-body and three-body chiral forces. An extended self-consistent Greens function formalism is defined t
o consistently incorporate three-body forces in the many-body calculations. The effect of three-nucleon interactions is included via the construction of a dressed two-body density dependent force. This is obtained performing an average of the leading order three-body terms in the chiral effective field theory expansion. The dressed force corresponds to the use of an in-medium propagator in the average which takes into account the correlations characterizing the system at each stage of the many-body calculation. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sumrule to correctly account for the effect of three-body forces. Microscopic as well as macroscopic properties of symmetric nuclear and pure neutron matter are analyzed in detailed.
